A piece of wire of a diameter 0.70 mm and length 1m has a total resistance of 2 ohms . Calculate the resistivity of the material of the wire .
p = RA/L
so plug in your numbers
To calculate the resistivity of the material of the wire, you will need to use the formula:
Resistivity (ρ) = (Resistance (R) x Cross-sectional Area (A)) / Length (L)
Given:
Diameter (d) = 0.70 mm = 0.0007 m
Length (L) = 1 m
Resistance (R) = 2 Ω
First, let's calculate the cross-sectional area (A):
Radius (r) = d/2 = 0.0007 m / 2 = 0.00035 m
Area (A) = π * r^2 = π * (0.00035 m)^2 = 3.85 x 10^-7 m^2
Now, we can use the formula to calculate the resistivity (ρ):
ρ = (R x A) / L = (2 Ω x 3.85 x 10^-7 m^2) / 1 m
ρ = 7.7 x 10^-7 Ω.m
Therefore, the resistivity of the material of the wire is 7.7 x 10^-7 Ω.m.
To calculate the resistivity of the material of the wire, we can use the formula:
R = (ρ * L) / A
where:
R = total resistance of the wire
ρ = resistivity of the material
L = length of the wire
A = cross-sectional area of the wire
First, we need to calculate the cross-sectional area of the wire. The wire has a diameter of 0.70 mm, so we can use the formula:
A = π * (d/2)^2
where:
A = cross-sectional area of the wire
d = diameter of the wire
Plugging in the values:
A = π * (0.70 mm / 2)^2
Calculating A gives us:
A = π * (0.35 mm)^2
Now, let's convert the diameter from millimeters to meters:
0.35 mm = 0.35 * 10^(-3) m
Plugging in the converted value for the diameter, we have:
A = π * (0.35 * 10^(-3) m)^2
Calculating A gives us:
A = 3.14 * (0.35 * 10^(-3) m)^2
Now, we have the cross-sectional area of the wire.
Next, we can rearrange the equation R = (ρ * L) / A to solve for ρ:
ρ = (R * A) / L
Plugging in the given values:
ρ = (2 ohms) * (3.14 * (0.35 * 10^(-3) m)^2) / (1 m)
Calculating ρ gives us:
ρ ≈ 6.66 * 10^(-8) ohm/m
Therefore, the resistivity of the material of the wire is approximately 6.66 x 10^(-8) ohm/m.